Certainly! Let's break down this question regarding Aaron's potential investment in his education into a step-by-step solution:
### Step 1: Understand the Costs
Aaron is considering obtaining an associate's degree, which will cost him [tex]$30,000 over 2 years.
### Step 2: Salary Comparison
We need to compare the median salary of a high school graduate and an associate's degree graduate. Let's assume:
- Median salary for a high school graduate (S_hs) is $[/tex]X per year.
- Median salary for an associate's degree holder (S_ad) is [tex]$Y per year.
### Step 3: Calculate the Additional Earnings
The difference in annual earnings between the two levels of education is:
\[
\Delta S = S_{ad} - S_{hs}
\]
This amount represents the additional income Aaron would earn each year after obtaining his associate's degree.
### Step 4: Compute Recovery Time
The recovery time for Aaron's $[/tex]30,000 investment can be calculated by dividing the total cost of education by the additional annual earnings:
[tex]\[
\text{Recovery Time} = \frac{\$30{,}000}{\Delta S}
\][/tex]
### Example with Hypothetical Salaries
Let's hypothetically set:
[tex]\[
S_{hs} = \$30{,}000 \quad \text{per year}
\][/tex]
[tex]\[
S_{ad} = \$40{,}000 \quad \text{per year}
\][/tex]
Then, the additional annual earnings ([tex]\(\Delta S\)[/tex]) are:
[tex]\[
\Delta S = \$40{,}000 - \$30{,}000 = \$10{,}000
\][/tex]
So, the recovery time is:
[tex]\[
\text{Recovery Time} = \frac{\$30{,}000}{\$10{,}000 \text{ per year}} = 3 \text{ years}
\][/tex]
### Conclusion
Based on our calculation, it would take Aaron 3 years to recover his $30,000 investment in his college education, assuming he continues to work full-time and starts earning the median salary for an associate's degree holder immediately upon graduation.
